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Black-Scholes calculator: option price and Greeks

Enter the stock price, strike, days to expiry, volatility and interest rate. You get the theoretical call and put prices and the main Greeks: delta, gamma, theta per day and vega.

How to use it

  1. Enter the stock price and the strike price.
  2. Enter days to expiry and implied volatility as a percent.
  3. Set the risk-free rate (about the current short-term Treasury yield).
  4. Read call and put prices, delta, gamma, theta per day and vega per 1% of volatility.
Call = S·N(d1) − K·e^(−rT)·N(d2) · d1 = [ln(S/K) + (r + σ²/2)T] ÷ (σ√T)
Example. Stock 100, strike 100, 365 days, volatility 20%, rate 5%: call ≈ $10.45, put ≈ $5.57, call delta ≈ 0.637.

About this calculator

The Black-Scholes model prices a European option from five inputs and also yields the Greeks, which measure how the price changes with the stock price (delta, gamma), time (theta) and volatility (vega). Listed US equity options are American-style and can be exercised early, and dividends are ignored here, so the output is a theoretical reference rather than a quote. Implied volatility is usually backed out of market prices, which is why the expected move calculator uses the same input.

Frequently asked questions

What is the Black-Scholes formula?
It prices a European call as S times N(d1) minus K times e to the minus rT times N(d2), where d1 and d2 come from the stock price, strike, time, volatility and interest rate.
What do delta, gamma, theta and vega mean?
Delta is the price change per $1 move in the stock, gamma is how fast delta changes, theta is the daily time decay, and vega is the price change per one percentage point change in implied volatility.
Is Black-Scholes accurate for stock options?
It is a standard reference model but assumes constant volatility, no dividends and European exercise. Real prices differ, especially for American options and around events.

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Informational calculator for reference only. Outputs are arithmetic, not quotes, recommendations or trade signals. LiquidityLevels provides educational market commentary, not financial advice.